Question

If $u$ and $v$ are unit vectors and $\theta$ is the acute angle between, then $2u\times 3v$is a unit vector for?

• A. exactly two values of $\theta$
• B. more than two values of $\theta$
• C. no value of $\theta$
• D. exactly one value of $\theta$

Answer 1

The correct option is D

exactly one value of $\theta$

Explanation for the correct answer:

To find the value of $\theta$:

If $2u\times 2v$ is a unit vector, then,

$\begin{array}{rcl}|2u\times 2v|& =& 1\\ 2\left|u\right|\left|v\right|\sin \theta & =& 1\\ Sin\theta & =& \frac{1}{6}\end{array}$

Therefore, there is exactly one value of $\theta$ for which $2u\times 3v$ is a unit vector.

Hence, the correct option is D.